And my problem is that questions like this are heavily downvoted. This isn't a bad question per se, even if it may be a little bit confused. As I understand, only a minority of people here are physicists, and quite a lot of people on LW haven't technical understanding of quantum theory. So the parent comment can't be perceived as ignorant of some already shared standard of rationality. Also, MWI is still not a broad scientific consensus today, even if some portray it such. So why does the parent stand at -5? Do we punish questioning the MWI? If so, why?

Now on topic. MWI doesn't violate thermodynamics any more than the Copenhagen interpretation. In the CI one can have a superposition of states of different energy collapsing into one of the involved energies; the estimated (mean) energy of the state is not conserved through the measurement.

The energy is conserved in two senses: first, it is conserved during the evolution of a closed system (without measurement), and second, it is conserved completely when using statistical mixed states to model the system - in this case, the collapse puts the system into a mixed state, and the mean value of any observable survives the collapse without change. Of course, the energy conservation requires time-independent dynamics (it means time-independence of the laws governing the system and all physical constants) in both cases.

An important technical point is that measurements always transfer the energy to the apparatus and therefore there is little sense to demand conservation of energy of the measured system during a measurement. To model a realistic measurement, the apparatus has to be described by a non-self-adjoint Hamiltonian to effectively describe dissipation, or at least it has to have a time-dependent Hamiltonian, or both; else, the apparatus will not remember the results. In both cases, energy conservation is trivially broken.

As for the (implicit) first question how the worlds are created: There is one Hilbert space consisting of all possible state vectors of the world. The state of the world can be, in a rough idealisation, decomposed into a tensor-product of smaller states of individual observers and non-observer subsystem (whether a subsystem is or isn't an observer is not particularly important, and it is probably related to the problem of consciousness). In a subspace of a particular observer, some states are specific, while most of the states aren't. The specific states correspond to certain thoughts. In an idealisation of an observer who cares only about one particular physical system, the observer's specific states all correspond to states of the system, which are said to have a sharp value of certain observables.

Now, in the Schrödinger picture, all state vectors evolve. Interaction between the observer and the observed system takes the state vectors into correlation. After that, the overall state vector of the observer+system compound can't be written as a tensor product of a observer-vector and a system-vector, and thus talking about the state of the observer alone doesn't make sense any more.

The consciousness of the observer works in such a way, that it decomposes the state of the observer+system into sum of vectors, each of which can be written as a tensor product of an observer-vector and a system-vector (although entire the sum can't), and lives a separate instance on each summand. Each of this instances forms what is called a world in the MWI jargon.

These worlds thus aren't created from void by some physical action. It's perhaps better to say that they are "interpreted into existence" by individual observers' consciousnesses. The division of the whole universe into individual worlds is observer dependent.

These worlds aren't being "created out of nowhere" as people imagine it. They are only called worlds because they are regions of the wavefunction which don't interact with other regions. It is the same wavefunction, and it is just being "sliced more thinly". To an observer, able to look at this from outside, there would just be the wavefunction, with parts that have decohered from each other, and that is it. To put it another way, when a world "splits" into two worlds, it makes sense to think of it as meaning that the "stuff" (actually the wavefunction) making up that world is divided up and used to make two new, slightly different worlds. There is no new "stuff" being created. Both worlds actually co-exist in the same space even: It is only their decoherence from each other that prevents interaction. You said that your problem is "how they (the worlds) are created" but there isn't anything really anything new being created. Rather, parts of reality are ceasing interaction with each other and there is no mystery about why this should be the case: Decoherence causes it.

How do You reconcile MWI with the 1st Law of thermodynamics?

Why do you see a conflict? You seem to be assuming both that the total energy of the universe is positive (not known!), and that each universe has the same total energy (i.e. that energy is not arbitrarily scalable). Why not assume that a universe with 100 joules of energy splits into two universes - one with 100 zorkmids of energy and the other with 100 arkbarks of energy (where it is understood that 1 zorkmid + 1 arkbark = 1 joule).

A better question - how does the observed 1st law of thermodynamics arise from the laws of physics underpinning the many worlds?

Erm, I can tell you less about physics than the creationist museum about evolution but I don't think it applies to open systems.

Anyway, for some interesting information about thermodynamics go here:

Mea Culpa: I was wrong; Eliezer was wrong; Sean Carroll was right.